# Robert Bryant

- Philip Griffiths Professor of Mathematics
- Professor in the Department of Mathematics

**External address:**103 Physics Bldg, West Campus, Durham, NC 27708

**Internal office address:**Box 90320, Durham, NC 27708-0320

**Phone:**(919) 660-2817

**Office Hours:**

Tuesdays and Thursdays, 10:30-12:00PM, and by appointment

### Research Areas and Keywords

##### Algebra & Combinatorics

##### Analysis

##### Computational Mathematics

##### Geometry: Differential & Algebraic

##### Mathematical Physics

##### PDE & Dynamical Systems

##### Topology

I'm interested in the geometry of partial differential equations (as always), but, more specifically, I have been thinking about conservation laws for PDE, Finsler geometry, calibrations, holonomy, and trying to learn more about Seiberg-Witten invariants and symplectic geometry.

Most recently, I have been named as the Director of the Simons Collaboration "Special Holonomy in Geometry, Analysis, and Physics", and so most of my research lately and in the near future will be directed towards problems in this area.

Bryant, RL. "Lie groups and twistor spaces." *Duke Math. J.* 52.1 (1985): 223-261.

Bryant, RL. "Minimal surfaces of constant curvature in S^n." *Trans. Amer. Math. Soc.* 290.1 (1985): 259-271.

Bryant, RL. "A duality theorem for Willmore surfaces." *J. Differential Geom.* 20.1 (1984): 23-53.

Berger, E, and Griffiths, P. "The Gauss equations and rigidity of isometric embeddings." *Duke Math. J.* 50.3 (1983): 803-892.

Griffiths, P, and Yang, D. "Characteristics and existence of isometric embeddings." *Duke Math. J.* 50.4 (1983): 893-994.

Bryant, RL. "Conformal and minimal immersions of compact surfaces into the 4-sphere." *J. Differential Geom.* 17.3 (1982): 455-473. (Academic Article)

Bryant, RL. "Submanifolds and special structures on the octonians." *J. Differential Geom.* 17.2 (1982): 185-232.

Bryant, RL. "Holomorphic curves in Lorentzian CR-manifolds." *Trans. Amer. Math. Soc.* 272.1 (1982): 203-221.

Berger, E, and Griffiths, P. "Some isometric embedding and rigidity results for Riemannian manifolds." *Proc. Nat. Acad. Sci. U.S.A.* 78.8 (1981): 4657-4660.

Bryant, RL, Foulon, P, Ivanov, S, Matveev, VS, and Ziller, W. "Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$." Open Access Copy